​

class Sod {

  constructor(f = 1, z = 1, r = 0) {

    this.k1 = 0;

    this.k2 = 0;

    this.k3 = 0;

    this.setWeights(f, z, r);

    this.value = 0;

    this.value_vel = 0;

    this._lastX = 0;

    this.accurate = false;

    this._crit = 0;

  }

  setK(k1 = this.k1, k2 = this.k2, k3 = this.k3) {

    this.k1 = k1;

    this.k2 = k2;

    this.k3 = k3;

    this._crit = 

      this.accurate && 0.8 * (Math.sqrt(4 * this.k2 + this.k1 ** 2) - this.k1);

    return this;

  }

  setWeights(f, z, r) {

    this.k1 = z / (Math.PI * f);

    this.k2 = 1 / (2 * Math.PI * f) ** 2;

    this.k3 = (r * z) / (2 * Math.PI * f);

    this._crit = 

      this.accurate && 0.8 * (Math.sqrt(4 * this.k2 + this.k1 ** 2) - this.k1);

    return this;

  }

  setAccuracy(v) {

    this.accurate = v;

    this._crit = 

      this.accurate && 0.8 * (Math.sqrt(4 * this.k2 + this.k1 ** 2) - this.k1);

    return this;

  }

  setValue(value) {

    this.value = value;

    return this;

  }

  getValue() {

    return this.value;

  }

  update(time, x, x_vel = null) {

    if (x_vel == null) {

      x_vel = (x - this._lastX) / time;

      this._lastX = x;

    }

    if (this.accurate) {

      const iterations = Math.ceil(time / this._crit);

      time = time / iterations;

      for (let i = 0; i < iterations; i++) {

        this.value += this.value_vel * time;

        const value_accel = 

          (x + this.k3 * x_vel - this.value - this.k1 * this.value_vel) / this.k2 ;

        this.value_vel += time * value_accel;

      }

    } else {

      this.value += this.value_vel * time;

      const newk2 = 

        Math.max(this.k2, 1.1 * (time ** 2 / 4 + time * this.k1 / 2)) ;

      const value_accel = 

        (x + this.k3 * x_vel - this.value - this.k1 * this.value_vel) / newk2 ;

      this.value_vel += time * value_accel;

    }

    return this.value;

  }

}

​

function setup() {

  createCanvas(512, 480);

  colorMode(HSB)

  background(0);

}

​

const pDot = {

  x: new Sod(4, 0.3, -2.5).setAccuracy(true),

  y: new Sod(4, 0.3, -2.5).setAccuracy(true),

};

const f = 60;

function draw() {

  frameRate(60);

  background(0, 0, 0, 0.01);

  stroke((millis() / 20) % 360, 120, 255)

  strokeWeight(8)

  for (let i = 0; i < 8; i++) {

    const lastPosx = pDot.x.value;

    const lastPosy = pDot.y.value;

    pDot.x.update(1/f /8, mouseX);

    pDot.y.update(1/f /8, mouseY);

    line(lastPosx, lastPosy, pDot.x.value, pDot.y.value)

  }

}